Spread spectrum modulation system and method for embedding digital information into digital or analog media

ABSTRACT

A system and method for embedding information into digital media and later detecting the embedded information using a unique spread spectrum modulation technique. In general, the present invention removes interference caused by an original signal from the detection process thereby eliminating a major source of detection error. The interference caused by the original signal is removed by using the encoder knowledge about the original signal and modulating the energy of the embedded mark to compensate for the original signal interference. The present invention also includes a novel redundant bit representation technique causes a resulting average over a large sample to tend to zero, thereby reducing the vulnerability of the present invention to malicious collusion attacks.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates in general to a system and methodfor digitally embedding information and, in particular, to a system andmethod for embedding digital information into digital or analog mediaand later detecting the embedded information using spread spectrummodulation.

[0003] 2. Related Art

[0004] Embedding digital information into a digital or analog media hasmany important applications including counterfeiting reduction. Forexample, copyright information may be hidden within a digital signal(such as an image, video or audio), distributed with the digital signaland then later detected to ensure authenticity. The technique ofembedding information within a work in a way that is not immediatelyperceptible and is hard to reproduce (also called “watermarking”) hasbeen used for centuries in applications such as documents and currency.In current times, the widespread digital representation of images,audio, video and other signals has led to the use of a “digitalwatermark” for copyright protection. This marking of digital mediainvolves hiding information under an original signal by embedding (oradding) an imperceptible signal (the mark) to the original signal.

[0005] Most marking techniques use existing spread spectrum modulationtechniques to modulate information (the mark) and embed the mark withinan original signal. For example, the bits composing the desired mark(such as the name of the copyright owner) are modulated using a spreadspectrum sequence and added to the original signal (such as a musicalwork in digital form). More often, the spread spectrum sequence is addedto a transformation of the original signal, which may be more sensitiveto manipulation. Typically, these existing spread spectrum modulationtechniques are robust to interfering noise so that the amount of energy(or distortion) that must be added to the marked signal to erase themark is quite high. This means that it is difficult remove the mark fromthe original signal.

[0006] In existing spread spectrum techniques, the original signal (alsoknown as a carrier signal) is seen as a source of noise. One problemwith these existing techniques is that, as a source of noise, theoriginal signal tends to interfere with the detection of the mark andreduce the mark detection accuracy. This is particularly a problembecause the original signal is generally much stronger than any otherinterference and therefore is the main source of interference.

[0007] One embedding technique that uses quantization index modulationdoes reduce interference from the original signal. The problem, however,with this technique is that the mark is embedded in a lattice, whichmakes the mark highly sensitive to amplitude scaling of the signal. Inother words, a slight change in the scale of the marked signal causesthe mark to be erased. This makes the quantization index modulationtechnique practically useless in applications where a malicious attackmay occur.

[0008] What is needed is a system and method for embedding informationinto a digital media that removes the original signal as a source ofinterference and obtains a large gain accurately detecting the markwithin the marked digital media. In particular, the system and methodwould subtract the influence of the original signal from the markthereby virtually eliminating a large portion of the interference.Elimination of this interference would greatly decrease error in themark detection rate and greatly increase performance. In addition, themarking system should be robust and insensitive to amplitude scaling andother forms of malicious attacks. Whatever the merits of theabove-mentioned systems and methods, they do not achieve the benefits ofthe present invention.

SUMMARY OF THE INVENTION

[0009] To overcome the limitations in the prior art as described aboveand other limitations that will become apparent upon reading andunderstanding the present specification, the present invention isembodied in a system and method for embedding digital information intodigital or analog media and later detecting the embedded informationusing a unique spread spectrum modulation technique. The novel spreadspectrum modulation technique is capable of removing any carrier signalinterference from the modulation. In particular, the present inventionsubtracts part or all of the interference from the original signalbefore transmission of a marked signal to enable superior detection ofany information embedded in the received signal.

[0010] The present invention provides several advantages that improvereliability over current spread spectrum techniques for embedding anddetecting information in digital media. In particular, unliketraditional spread spectrum techniques, in the present invention thecarrier signal does not act as a noise source because the carrier signalinterference is removed beforehand from the received signal. Thispermits the present invention to achieve significant performanceimprovements over traditional spread spectrum techniques. Improvedperformance afforded by the present invention greatly reduces theinstances of misdetection of the embedded information. In addition, thepresent invention maintains the robustness of traditional spreadspectrum techniques while achieving higher noise robustness gain andprovides security against malicious attacks.

[0011] In general, the method of the present invention obtains areceived signal on which information is to be embedded. The presentinvention then obtains information about the expected interference fromthe original signal upon a watermark detector. The present inventionthen removes all or part of this interference while simultaneouslyembedding the desired mark within the signal. Estimation of the amountof watermark signal to embed or remove is performed using a genericfunction that minimizes the probability of error in the detection of theembedded information. In one embodiment of the invention, the genericfunction is approximated as a linear function and in an alternateembodiment the generic function is a non-linear function. Moreover,distortion parameters may be introduced in this generic function tocontrol distortion levels. Other enhancements are included within thepresent invention such as, for example, the introduction of a smallrandomization into the distortion parameters to provide a more securedetection method.

[0012] The present invention also includes a method of reducing thevulnerability of unwanted embedded information removal. In particular,the present invention includes a novel redundant bit representationtechnique causes a resulting average over a large sample to tend tozero. In a preferred embodiment, the present invention inserts an“invert” bit having a 50% probability to indicate the need to invert anyremaining bits. Several other redundant representations may be used withthis method to achieve similar results. The present invention alsoincludes a system of embedding and detecting information in digitalmedia that utilizes the methods of the present invention.

[0013] Other aspects and advantages of the present invention as well asa more complete understanding thereof will become apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, illustrating by way of example the principles ofthe invention. Moreover, it is intended that the scope of the inventionbe limited by the claims and not by the preceding summary or thefollowing detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The present invention can be further understood by reference tothe following description and attached drawings that illustrate thepreferred embodiments. Other features and advantages will be apparentfrom the following detailed description of the invention, taken inconjunction with the accompanying drawings, which illustrate, by way ofexample, the principles of the present invention.

[0015] Referring now to the drawings in which like reference numbersrepresent corresponding parts throughout:

[0016]FIG. 1 is a block diagram illustrating an apparatus for carryingout the present invention.

[0017]FIG. 2A is a general block diagram illustrating an embeddingsystem and method in accordance with the present invention.

[0018]FIG. 2B is a general block diagram illustrating a detecting systemand method in accordance with the present invention.

[0019]FIG. 3 is a general flow diagram of a digital embedding method ofthe present invention.

[0020]FIG. 4 is a detailed block diagram illustrating a working exampleof FIGS. 2 and 3 of the present invention.

[0021]FIG. 5 is a plot of the error probability as a function of the SNR(signal-to-noise ratio) in the detection variable.

[0022]FIG. 6 is a plot of the error probability as a function of thesecond linear embedding parameter.

[0023]FIG. 7 is a plot illustrating a method of the present inventionfor solving for the optimum generic embedding function.

DETAILED DESCRIPTION OF THE INVENTION

[0024] In the following description of the invention, reference is madeto the accompanying drawings, which form a part thereof, and in which isshown by way of illustration a specific example whereby the inventionmay be practiced. It is to be understood that other embodiments may beutilized and structural changes may be made without departing from thescope of the present invention.

[0025] I. Exemplary Operating Environment

[0026]FIG. 1 and the following discussion are intended to provide abrief, general description of a suitable computing environment in whichthe invention may be implemented. Although not required, the inventionwill be described in the general context of computer-executableinstructions, such as program modules, being executed by a computer.Generally, program modules include routines, programs, objects,components, data structures, etc. that perform particular tasks orimplement particular abstract data types. Moreover, those skilled in theart will appreciate that the invention may be practiced with a varietyof computer system configurations, including personal computers, servercomputers, hand-held devices, multiprocessor systems,microprocessor-based or programmable consumer electronics, network PCs,minicomputers, mainframe computers, and the like. The invention may alsobe practiced in distributed computing environments where tasks areperformed by remote processing devices that are linked through acommunications network. In a distributed computing environment, programmodules may be located on both local and remote computer storage mediaincluding memory storage devices.

[0027] With reference to FIG. 1, an exemplary system for implementingthe invention includes a general-purpose computing device in the form ofa conventional personal computer 100, including a processing unit 102, asystem memory 104, and a system bus 106 that couples various systemcomponents including the system memory 104 to the processing unit 102.The system bus 106 may be any of several types of bus structuresincluding a memory bus or memory controller, a peripheral bus, and alocal bus using any of a variety of bus architectures. The system memoryincludes read only memory (ROM) 110 and random access memory (RAM) 112.A basic input/output system (BIOS) 114, containing the basic routinesthat help to transfer information between elements within the personalcomputer 100, such as during start-up, is stored in ROM 110. Thepersonal computer 100 further includes a hard disk drive 116 for readingfrom and writing to a hard disk, not shown, a magnetic disk drive 118for reading from or writing to a removable magnetic disk 120, and anoptical disk drive 122 for reading from or writing to a removableoptical disk 124 such as a CD-ROM or other optical media. The hard diskdrive 116, magnetic disk drive 118 and optical disk drive 122 areconnected to the system bus 106 by a hard disk drive interface 126, amagnetic disk drive interface 128 and an optical disk drive interface130, respectively. The drives and their associated computer-readablemedia provide nonvolatile storage of computer readable instructions,data structures, program modules and other data for the personalcomputer 100.

[0028] Although the exemplary environment described herein employs ahard disk, a removable magnetic disk 120 and a removable optical disk124, it should be appreciated by those skilled in the art that othertypes of computer readable media that can store data that is accessibleby a computer, such as magnetic cassettes, flash memory cards, digital-video disks, Bernoulli cartridges, random access memories (RAMs),read-only memories (ROMs), and the like, may also be used in theexemplary operating environment.

[0029] A number of program modules may be stored on the hard disk,magnetic disk 120, optical disk 124, ROM 110 or RAM 112, including anoperating system 132, one or more application programs 134, otherprogram modules 136 and program data 138. A user (not shown) may entercommands and information into the personal computer 100 through inputdevices such as a keyboard 140 and a pointing device 142 as well asother input devices (not shown) including, for example, a microphone,joystick, game pad, satellite dish, scanner, or the like. These otherinput devices are often connected to the processing unit 102 through aserial port interface 144 that is coupled to the system bus 106, but maybe connected by other interfaces, such as a parallel port, a game portor a universal serial bus (USB). A monitor 146 or other type of displaydevice is also connected to the system bus 106 via an interface, such asa video adapter 148. In addition to the monitor 146, personal computerstypically include other peripheral output devices (not shown), such asspeakers and printers.

[0030] The personal computer 100 may operate in a networked environmentusing logical connections to one or more remote computers, such as aremote computer 150. The remote computer 150 may be another personalcomputer, a server, a router, a network PC, a peer device or othercommon network node, and typically includes many or all of the elementsdescribed above relative to the personal computer 100, although only amemory storage device 152 has been illustrated in FIG. 1. The logicalconnections depicted in FIG. 1 include a local area network (LAN) 154and a wide area network (WAN) 156. Such networking environments arecommonplace in offices, enterprise-wide computer networks, intranets andthe Internet.

[0031] When used in a LAN networking environment, the personal computer100 is connected to the local network 154 through a network interface oradapter 158. When used in a WAN networking environment, the personalcomputer 100 typically includes a modem 160 or other means forestablishing communications over the wide area network 156, such as theInternet. The modem 160, which may be internal or external, is connectedto the system bus 106 via the serial port interface 144. In a networkedenvironment, program modules depicted relative to the personal computer100, or portions thereof, may be stored in the remote memory storagedevice 152. It will be appreciated that the network connections shownare exemplary and other means of establishing a communications linkbetween the computers may be used.

[0032] II. Introduction

[0033] Spread spectrum is a communication technique that uses wide band,noise-like signals. Because spread spectrum signals resemble noise, theyare hard to detect, difficult to interfere with and hard to decode. Ingeneral, spread spectrum includes a transmission station having anencoder that encodes data to produce an intermediate signal having arelatively narrow bandwidth centered around a certain frequency. Inorder to increase the bandwidth of the signal transmitted, thisintermediate signal is modulated using a sequence of pseudorandomnumbers created by an algorithm. The transmission station shares thealgorithm with a receiving station because, unless the algorithm isknown, the sequence is virtually impossible to predict. Upon receptionby the receiving station, the same pseudorandom sequence created by theknown algorithm is used to demodulate the spread spectrum signal and adecoder is used to recover the encoded data.

[0034] The present invention includes an embedding system and methodthat removes interference caused by the original signal from thedetection process. Using a unique spread spectrum modulation technique,the present invention virtually eliminates distortion caused by theoriginal signal, thereby improving performance. The interference causedby the original signal is removed by using the encoder knowledge aboutthe original signal and modulating the energy of the embedded mark tocompensate for the original signal interference. This unique spreadspectrum modulation technique provides exceptional improvement overexisting spread spectrum techniques and may be readily implementedwithin most marking systems using spread spectrum, thereby providingimproved performance.

[0035] The method and system of the present invention includes severalembodiments that may be used depending on the application. Morespecifically, one embodiment includes a novel spread spectrum modulationtechnique that uses a linear generic embedding function. This linearapproximation reduces the embedding complexity while still providingsignificantly improved detection of the mark over present spreadspectrum techniques. Another embodiment of the present invention limitsthe distortion level to a desired distortion level by removing theinfluence of the original signal x from the detection over a pre-definedrange of the original signal x. Still another embodiment does notrestrict the generic embedding function to a linear function. Thisnonlinear embodiment is more complex and more generic that the linearapproximation embodiment. Moreover, the present invention includes aredundant bit representation technique that is implemented so that aresulting average of marks tends to zero when several original signalsare averaged together.

[0036] III. General Overview

[0037] The present invention is embodied in a system and method forembedding digital information into digital or analog media and laterdetecting the embedded information using spread spectrum modulation.Embedding the desired information includes removing an original signal(such as a digital sound, video or image file) as a source ofinterference to improve the detection process. The original signal isknown to the encoder but is generally treated as a source ofinterference. Removing the interference from the original signal (usingthe method of the present invention described herein) produces adramatic improvement in the detection of the embedded information. Thedetection technique of the present invention uses spread spectrummodulation and knowledge about the original signal to enhance detectionperformance by modulating the energy of the embedded information tocompensate for the interference of the original signal.

[0038]FIGS. 2A and B are general block diagrams illustrating a systemand method for embedding digital information into digital or analogmedia in accordance with the present invention. In general, the systemand method of the present invention includes embedding digitalinformation into digital or analog media and later detecting thatembedded information. The embedded information can be a series of bitsthat, when embedded into an original signal, provide a unique anddiscrete stamp (or mark) on the original signal that, for example, mayprovide copyright owner information about the original signal. Embeddedinformation is added under the original signal (the original signal is“marked”) such that the embedded information is difficult to detect andvirtually imperceptible except to a detector.

[0039] A general system and method for an embedding portion of spreadspectrum-based watermarking is shown in FIG. 2A. In particular, anoriginal signal 205 is received by an embedder 210. An embeddertransform process 220 is applied to the original signal 205. Asdiscussed in detail below, the embedder transform process 220 convertsthe original signal 205 to a domain more appropriate to the watermarkinsertion. The embedder transform process 220 produces a transformedsignal x 225 which is input to an embedding process 230. The embeddingprocess 230 receives as input the transformed signal x 225, a secret key215 (K$), and a bit to be inserted (or information) b 217. Next, theembedding process 230 produces an output signal s 235 that is thenpassed on to an inverse transformation process 240. The inversetransformation process 240, which performs the inverse transformation ofthe embedder transform process 220, produces a watermarked signal 245.The watermarked signal 245 is similar to the original signal 205 exceptthat the watermarked signal 245 contains the information b hidden in thewatermarked signal 245.

[0040] A general system and method for a detecting portion of spreadspectrum-based watermarking is shown in FIG. 2B. A detector 260 receivesa received signal 255 (which may differ slightly from the watermarkedsignal 245 due to channel noise, compression, or attack noise) and usesthe present invention to obtain a signal y 265 that is as close to theoutput signal s 235 as possible. This includes applying a detectortransformation process 270 (which may be similar or identical to theembedder transform process 220) and a filtering and re-syncing process280, which removes or reduces any eventual noise added to the signal orshifts that may have occurred. Based on the signal y 265, a detectionprocess 290 verifies the presence of the mark and detects a transmittedbit {circumflex over (b)} 275. In order to achieve this detection, thedetection process 290 generally makes use of a copy of the secret key K$215. Ideally, the watermarked signal 245 is indistinguishable from theoriginal signal 205, but the mark can be detected and decoded by thedetector 260 even if the watermarked signal 245 is processed orotherwise modified.

[0041] In general, the embedder transform process 220 represents atransform from an original signal domain to a domain where the data ismore equally sensitive to tampering. Ideally, this “good transform” alsoremoves any part of the data that is not perceptually significant. Inthe case of images, for example, the transform should be virtuallyinsensitive to translation, small contrast manipulations, low-passfiltering, and other common signal processing techniques. The idea isthat, after the transform, any significant change in the signal wouldsignificantly impair the image. It should be noted that although a boxwith the inverse transformation process 240 is included, the transformdoes not need to strictly be invertible because some side informationcan be passed from the original signal to the inverse transform.

[0042] In general, the contents and design of boxes 220, 240, 270 and280 have been widely investigated and hundreds of examples exist in theliterature. In most of these cases, box 230 is implemented by simplyadding a spread spectrum modulated watermark to the signal and box 290is implemented as simply a spread spectrum detector. The improved spreadspectrum system and method of the present invention address mainly theimplementation of the embedding process 230. In fact, the presentinvention may be implemented readily into most of these hundreds ofwatermarking schemes by adopting whichever implementation of boxes 220,240, 270 and 280. Moreover, in many cases even the detection process 290may be imported directly from existing spread spectrum watermarkingsystems.

[0043] Consequently, the remainder of this application will consider thetransformed signal x 225 as the original signal. In addition, the neteffect of channels and attack noises combined with the effect of boxes240, 270 and 280 will be considered and will be denoted aschannel/attack noise n. In other words, channel/attack noise will bedefined as the part of the noise that was not canceled out by theprocesses of boxes 240, 270 and 280.

[0044] IV. General Operation of the Invention

[0045]FIG. 3 is a general flow diagram of a digital embedding method ofthe present invention. In general, the present invention includes anencoder for embedding a mark in to an original signal, and a detectorfor detecting the mark within a received signal. The encoder includeshaving the original signal received by a marking device (box 310),estimating the interference that this particular signal would have inthe detection process (box 320), and using this information to decideabout the strength (i.e., amplitude) of the mark to be added to thesignal (box 330), and then adding a mark (for example a pseudo randomchip sequence) to the original signal (box 340). A marked signal, whichincludes the mark embedded into the original signal, is then availablefor further processing (box 350). This processing may include, forexample, storage in a within a storage media and transfer (such astransmission over a network).

[0046] The detector of the present invention receives the marked signal(box 360), and proceeds to detect and decode the watermark by computinga correlation measure between the received signal and the chip sequence(box 370). By using information about the original signal available atthe encoder, the novel system and method of the present invention isable to reduce the probability of error in the detection of the mark andprovides improved performance over existing spread spectrum modulationtechniques.

[0047] V. Details of the Invention and Working Example

[0048] The present invention includes several embodiments that utilize aunique spread spectrum modulation technique that removes the influenceof the original signal from the detection process. More specifically,knowledge about the original signal from the encoder is used to removethe original signal during the detection process, thereby greatlyimproving performance. The following discussion provides details workingexamples of these embodiments of the present invention.

[0049]FIG. 4 is a detailed block diagram illustrating a working exampleof FIGS. 2 and 3 of the present invention. In FIG. 4, block 230represents the embedder encoder or watermark inserter), while block 290represents the detector (decoder or watermark detector). In this workingexample, information is embedded and detected in accordance with theunique spread spectrum modulation technique of the present invention. Ingeneral, the present invention obtains an original signal x (such assamples of a music, or coefficients of a transform of a segment of thatmusic) and embeds imperceptible information into the original signal xfor marking purposes. As shown in FIG. 4, the information preferably isgenerated using a pseudo-random number generator (PRN) 410 and a secretkey K$. This secret key is known by both the encoding process and thedetection of the present invention.

[0050] A unique and discrete mark (information or “chip sequence”) u isproduced from the secret key K$ and the PRN 410. An encoding bit b,which determines whether the chip sequence u is added or subtracted tothe original signal x, is provided to the encoder 230 and encoded aspart of the marking process. An amplitude embedding regulator 415decides the strength of the sequence to be inserted in the signal. Asexplained in detail below, the present invention includes severalembodiments of the unique spread spectrum modulation technique tomodulate the amplitude of the embedded chip sequence to compensate forinterference of the original signal. In a general form, the amplitude μof the embedded chip sequence will be a function of the bit to betransmitted b, and the correlation between the original signal x and thechip sequence u, this correlation is denoted herein by x, and which iscomputed by a correlation estimator 425. The final result of the processis a marked signal s, which is then sent to the receiver. Before thesignal reaches the detector noise n (such as channel noise or attacknoise) may be added to the marked signal s, and will generally increasethe probability of error in detecting b.

[0051] The decoder 290 shown in FIG. 4 determines the transmitted bit bembedded in the signal by verifying the sign of the discrete mark (inthe form of the chip sequence u) contained within marked signal s. Inthe present invention, this is done in a manner similar to traditionalspread spectrum (i.e. by computing a correlation measure between thereceived signal y and the chip sequence u, and evaluating the sign ofthis correlation). This is done in FIG. 4 by first computing thecorrelation between y and u at a correlation detector 430, and takingthe sign of the result in a sign detector 440. As will be explained inthe mathematical description that follows, this is equivalent toevaluating the sign of the sufficient statistic r. The chip sequence uis obtained by using the secret key K$ and a copy of a number generator460, which is a copy of the number generator used by the encoder 230. Incase the embedded watermark consists of more than one bit, the processis repeated for each segment of the sequence u corresponding to each bitof the watermark, as in a traditional spread spectrum technique.

[0052] The mathematical details of FIG. 4 will now be discussed. Inparticular, the chip sequence u produced by the secret key K$ and thePRN 410 has a zero mean and elements that are equal to +s_(u) or −s_(u).This chip sequence u is then added or subtracted to the original signalx according to the encoding bit b, where b is equal to either +1 or −1.The encoding bit b is transmitted with the marked signal s.

[0053] An analysis of spread spectrum modulation as applied to embeddinginformation into digital media leads to a formula for a probability oferror. Initially, the inner product and norm are defined as:${{\langle{x,u}\rangle}\overset{\Delta}{=}{\frac{1}{N}{\sum\limits_{i = 0}^{N - 1}\quad {x_{i}u_{i}}}}},{{{and}\quad {x}}\overset{\Delta}{=}{\langle{x,x}\rangle}},$

[0054] where N is the length of the vectors x, u, s, n, and y as shownin FIG. 4. An assumption is made that one bit of information is beingembedded into the marked signal s having N transform coefficients. Inthis case, the bit rate is 1/N bits/sample. The bit is represented bythe encoding bit b, whose value is variable and may be either −1 or +1.Whenever more than 1 bit is to be transmitted, the signal can be dividedup into as many parts as bits to be transmitted. Therefore, and withoutloss of generality, only the one bit case is considered in thisanalysis.

[0055] The present invention embeds the encoding bit b by adding thechip sequence u to the original signal x while modulating the energy ofthe inserted chip sequence u to compensate for interference from theoriginal signal x. Specifically, the present invention varies theamplitude of the embedded chip sequence u by a generic embeddingfunction μ(x,b), where, x

<x,u>/<u,u>. As discussed further below, this generic embedding functionμ may be linear or nonlinear and the general idea is to find a genericembedding function μ that minimizes the error of the encoding bit. Inother words, a generic embedding function is found that improves improveerror probability that the mark will be detected.

[0056] The embedding process of the present invention may be representedby:

s=x+m(x,b)u,

[0057] where, x

<x,u>/<u,u>. Note the distinction between the real-valued variable x andthe vector x. The present invention includes several embodiments of thisnovel embedding technique that are discussed in detail below.

[0058] Traditional Spread Spectrum Approximation for the EmbeddingFunction

[0059] For comparison reasons, the probability error of the embeddingprocess when using the traditional Spread Spectrum Modulation is firstanalyzed. This corresponds to approximating the embedding function by aconstant (i.e., by making μ=b). The associated probability error isanalyzed as follows.

[0060] A distortion D in the marked signal s is defined by ∥s−x∥. Thisleads to a distortion for the above embedding process of,

D=∥bu∥=∥u∥=S _(u) ².

[0061] The channel model may be represented as

y=s+n.

[0062] The present invention detects the embedded information (the chipsequence u) within the marked signal s by first computing a (normalized)sufficient statistic r.

r

<y,u>/<u,u>=<bu+x+n,u>/s _(u) ² =b+x+n,

[0063] and estimating the detected encoding bit by

{circumflex over (b)}=sign(r),

[0064] where x

<x,u>/<u,u> and n

<n,u>/<u,u>.

[0065] Even though the improvements obtained by the present inventionapply to generally any signal and noise distribution, for thismathematical analysis, both the original signal x and the noise n areassumed to be samples from uncorrelated white Gaussian random processes.Therefore, the original signal x and the noise n may be represented as

x _(i) ˜N(0,s _(x) ²), n _(i) ˜N(0,s _(n) ²)

[0066] In this case, the sufficient statistic r is also Gaussian,

r˜N(m _(r) ,s _(r) ²), m _(r) =E[r]=b s _(r) ²=(s _(x) ² +s _(n) ²)/N s_(u) ².

[0067] In the case where the encoding bit b=1, an error occurs when r<0,and so the error probability p is given by:$p = {{P\quad r\left\{ {\left. {\hat{b} < 0} \middle| b \right. = 1} \right\}} = {{\frac{1}{2}{{erfc}\left( \frac{m_{r}}{s_{r}\sqrt{2}} \right)}} = {\frac{1}{2}{{erfc}\left( \sqrt{\frac{s_{u}^{2}N}{2\left( {s_{x}^{2} + s_{n}^{2}} \right)}} \right)}}}}$

[0068] The same error probability is obtained under the assumption thatthe encoding bit b=−1. A plot of this probability as a function of thesignal-to-noise ratio m_(r)/s_(r) is shown in FIG. 5. In general, toachieve an error probability p means that

Ns _(u) ²>2(erfc ⁻¹(p))²(s _(x) ² +s _(n) ²).

[0069] The above equation above shows that the length of the chipsequence, N, can be traded with the energy of the sequence s_(u) ². Theequation allows computation of either N or s_(u) ² given the othervariables involved. As an example, as can be seen from FIG. 5, if anerror probability better than 10⁻³ is desired then we need

m _(r) /s _(r)>3

Ns_(u) ²>9(s_(x) ² +s _(n) ²).

[0070] It should be observed, therefore, that achieving a certain errorprobability when using traditional spread spectrum requires eitherincreasing the energy of the inserted mark (thereby increasingdistortion) or increasing the number of samples used to transmit eachbit of the mark (thereby reducing the channel capacity for the mark).The present invention is now analyzed, in which a significant reductionin error rates can be produced when compared with traditional spreadspectrum techniques.

[0071] Linear Approximation for the Generic Embedding Function

[0072] As discussed above, traditional spread spectrum techniquesapproximate the embedding function μ by a constant. One way of improvingperformance of the embedding is to find a generic embedding function μ,for example the one that minimizes the probability of error in thedetection of the encoded bit. A preferred embodiment of the presentinvention uses a linear approximation of the generic embedding functionμ. This linear approximation reduces the embedding complexity whilestill providing significantly improved detection over present spreadspectrum techniques. As discussed further below, even when the genericembedding function μ is approximated as a linear function theperformance (such as robustness to noise) of the spread spectrummodulation system and method of the present invention is comparable orsuperior to other types of spread spectrum techniques.

[0073] In this preferred embodiment the generic embedding function μ islinear and the embedding process of the present invention may berepresented as

s=x+(ab−1x)u

[0074] A first linear embedding parameter a and a second linearembedding parameter 1 control the distortion level and the removal ofthe carrier distortion on the detection statistic. It should be notedthat traditional spread spectrum techniques are obtained by setting thefirst and second linear embedding parameters to one and zero (a=1 and1=0), respectively, as done in the analysis in the previous section.

[0075] Using a similar noise model and same notation as above, thereceiver sufficient statistic r is

r=<y,u>/<u,u>=ab+(1−1)x+n.

[0076] It should be remembered that the term x represents the influence(interference) of the original signal x on the detection process. Thisequation shows that the closer the second linear embedding parameter 1is to 1, the more the influence of the original signal x will be removedfrom r. In other words, the closer 1 is to 1 the less influence theoriginal signal magnitude x has on receiver sufficient statistic r. Inaddition, the detected encoding bit remains unchanged in this linearapproximation embodiment and is equal to the sign(r).

[0077] The expected distortion of this linear embodiment of the presentinvention is given by${E\lbrack D\rbrack} = {{E\left\lbrack {{s - x}} \right\rbrack} = {{E\left\lbrack {{{{a\quad b} - {l\quad x}}}^{2}s_{u}^{2}} \right\rbrack} = {\left( {a^{2} + \frac{l^{2}s_{x}^{2}}{N\quad s_{u}^{2}}} \right){s_{u}^{2}.}}}}$

[0078] In order to make the average distortion of this linear embodimentapproximately equal that of traditional spread spectrum, the expecteddistortion is set to E[D]=s_(u) ², and therefore:$a = \sqrt{\frac{{N\quad s_{u}^{2}} - {l^{2}s_{x}^{2}}}{N\quad s_{u}^{2}}}$

[0079] Now the error probability may be computed using the mean andvariance of the sufficient statistic r. These are given by

m _(r) =ab s _(r) ²=(s _(n) ²+(1−l)² s _(x) ²)/Ns _(u) ².

[0080] Using this information, the error probability p for this linearembodiment is computed as$p = {{\Pr \left\{ {\left. {\hat{b} < 0} \middle| b \right. = 1} \right\}} = {{\frac{1}{2}{{erfc}\left( \frac{m_{r}}{s_{r}\sqrt{2}} \right)}} = {\frac{1}{2}{{{erfc}\left( \sqrt{\frac{{N\quad s_{u}^{2}} - {l^{2}s_{x}^{2}}}{2\left( {s_{n}^{2} + {\left( {1 - l} \right)^{2}s_{x}^{2}}} \right)}} \right)}.}}}}$

[0081] Alternatively, the error probability p may written as a functionof the relative power of the spread spectrum sequence, Ns_(u) ²/s_(x) ²,and the signal to noise ratio s_(x) ²/s_(n) ².$p = {\frac{1}{2}{{{erfc}\left( {\frac{s_{u}}{\sqrt{2}}\sqrt{\frac{{N\quad {s_{u}^{2}/s_{x}^{2}}} - l^{2}}{{s_{n}^{2}/s_{x}^{2}} + \left( {1 - l} \right)^{2}}}} \right)}.}}$

[0082]FIG. 6 is a plot of the error probability p as a function of thesecond linear embedding parameter l for various values of thesignal-to-noise ration (SNR) and Ns_(u) ²/s_(x) ². Solid lines representa 10 decibel (dB) SNR and dashed lines represent a 7 dB SNR. Each of thethree solid and three dashed lines correspond to values of Ns_(u)²/s_(x) ² equal to 5, 10 and 20 (such that higher values of Ns_(u)²/s_(x) ² have smaller error probability). It should be noted that whenthen the second linear embedding parameter equals zero (l=0) thiscorresponds to traditional spread spectrum techniques.

[0083]FIG. 6 shows that by proper selection of the second linearembedding parameter l, the error probability p for this linearembodiment can be made several orders of magnitude better thantraditional spread spectrum techniques. For example, referring to FIG.6, with a signal to interference ratio of 10 (i.e., 10 dB), there is areduction in the error rate from p₀=1.00e−5 for traditional spreadspectrum techniques to p=1.55e−43 for the linear embodiment of thepresent invention. This is a reduction of over 37 orders of magnitude inthe error probability. Higher SNR (as is common in practicalapplications) may yield even higher gains.

[0084] As can be inferred from FIG. 6, the error probability varies withl, with the optimum value usually close to one. The expression for theoptimum value for l can be computed from the error probability p bysetting ∂/∂l=0, and is:$l_{opt} = {\frac{1}{2}{\left( {\left( {1 + \frac{s_{n}^{2}}{s_{x}^{2}} + \frac{N\quad s_{u}^{2}}{s_{x}^{2}}} \right) - \sqrt{\left( {1 + \frac{s_{n}^{2}}{s_{x}^{2}} + \frac{N\quad s_{u}^{2}}{s_{x}^{2}}} \right)^{2} - {4\frac{N\quad s_{u}^{2}}{s_{x}^{2}}}}} \right).}}$

[0085] Note also from the above equation that, for N large enough, theoptimal value for the second linear embedding parameter approaches oneas the SNR approaches infinity (l_(opt)→1 as the SNR→∞).

[0086] Alternate Embodiments Using the Linear Generic Embedding Function

[0087] Two alternate embodiments of the present invention use the linearapproximation for the generic embedding function and modify the firstand second linear embedding parameters. Each one of these embodimentsmay be important for some applications and help to tailor the presentinvention for a particular application.

[0088] One of these alternate embodiments simplifies the embeddingprocess by choosing the second linear embedding parameter λ equal to one(λ=1). This choice simplifies embedding computations and increasesefficiency of the embedding process. Another alternate embodimentincludes also choosing the first linear embedding parameter equal to one(α=1). This choice further simplifies computation and increaseefficiency of the embedding process because the amplitude of the uniqueand discrete mark can be absorbed by s_(u) ².

[0089] Although the above alternate embodiments simplify computation andincrease efficiency, these embodiments may introduce an additionalweakness to the system. In particular, when the second linear embeddingparameter equals one (λ=1), the influence of the original signal on themarked signal is completely removed. This information can be used by anattacker to reduce the search space needed to detect the unique anddiscrete mark. Another alternate embodiment of the present inventionthat uses the linear approximation for the generic embedding functionaddress this concern by introducing a randomness in the second linearembedding parameter λ in order to remove the possibility of this attackon the marked signal. By introducing a small randomization in the secondlinear embedding parameter λ, the possibility of an attack on the markedsignal is essentially removed.

[0090] Limited Distortion Embedding Technique

[0091] In general, existing spread spectrum techniques have a constantaverage distortion level. Embodiments of the spread spectrum embeddingsystem of the present invention discussed above use a choice of thefirst and second linear embedding parameters (a and l) that guaranteethe same level of average distortion as in existing spread spectrumtechniques. The spread spectrum system and method of the presentinvention, however, does not have a constant average distortion level.In order to address this issue, the present invention includes anembodiment that limits the distortion to a desired maximum whilemaintaining the previously mentioned.advantages of this spread spectrumsystem and method.

[0092] In particular, the limited distortion embodiment of the presentinvention provides improved performance and efficiency in detection ofan embedded unique and discrete mark within a marked signal whileremoving the original signal x as a source of interference. By removingthe influence of the original signal x from the detection, thedistortion level may be limited while still providing improved detectionperformance. In addition, a desired distortion level may be selected inthis limited distortion embodiment. This is accomplished by removing theinfluence of the original signal x from the detection only over apre-defined range of the original signal x.

[0093] Limiting the distortion level does not necessarily affect anerror detection rate of the mark. In fact, by introducing a limit on thedistortion level, further improvement may be obtained in the errordetection rate. In particular, by looking at extremes of the distortionin the spread spectrum system and method of the present invention it isnoted that large values of distortion occur in two different situations.In one situation the sign of the influence of the original signal x isthe same as the sign of the encoding bit b. If λx/αb>1, then the secondlinear embedding parameter λ has an effect of reducing the strength ofthe unique and discrete mark. In other words, by setting (αb−λx)=0whenever λx/αb>1, the distortion can be made to equal zero and bettererror detection rates can be obtained because the mark will in fact bestronger.

[0094] In a second situation the influence of the original signal x andthe encoding bit b have opposite signs and the presence of the originalsignal acts to reduce the energy of the unique and discrete mark. Inthis case, the second linear embedding parameter λ helps to restore themark to an ideal level. In fact, if λ=1, the mark is always present atthe same energy level, regardless of the value of x. As explained above,however, the choice of the second linear embedding parameter equal toone (λ=1) is not the optimum choice for every application. If the secondlinear embedding parameter is less than one (λ<1) then there will be avalue of x above which the unique and discrete mark will not becorrectly detected even in the absence of noise. More precisely, if${\frac{x}{b} < \frac{- a}{\left( {1 - l} \right)}},$

[0095] then there is erroneous detection of the mark even in the absenceof noise. These are large values for the influence of the originalsignal x and therefore imply a large distortion level. Because the markis not going to be detected anyway, setting distortion equal to zero(i.e., αb−λx=0) is generally the preferred choice.

[0096] Therefore, although previous embodiments have assumed anunbounded distortion model to simplify mathematical analysis, anembodiment that uses a bound for the second linear embedding parameter λis used to produce a limited distortion embedding process. The choice ofthe second linear embedding parameter λ can be summarized as:$l = \left\{ \begin{matrix}l_{0} & {{{if}\quad - \frac{a}{\left( {1 - l_{0}} \right)}} < {b\quad x} < \frac{a}{l_{0}}} & \quad \\\frac{a\quad b}{x} & {{otherwise}\quad} & \quad\end{matrix} \right.$

[0097] where l₀ is the pre-computed value for the second linearembedding parameter λ as optimized by the previously described methods.It should be noted that this second choice for the second linearembedding parameter λ for when the original signal x is outside a giveninterval implies zero distortion. This embodiment may be seen as “givingup” whenever the original signal x is too large in the oppositedirection of the encoding bit b, and allowing a stronger mark wheneverthe original signal x is too strong but in the same direction as theencoding bit b. In these cases, we do not transmit the mark because thedistortion necessary to allow reception would be too high (as in thefirst case), or because the mark will be correctly detected even if itis not transmitted (as in the second case).

[0098] Even though the error detection rate may be improved byintroducing a limit on the distortion level as described above, onedisadvantage is that this limit is not under our control and the limitdepends only on the values established for the first and second linearembedding parameters (α and λ). In a preferred embodiment of the presentinvention, distortion is limited to a desired level by introducing awindow function to strictly control the limit of distortion. In thisway, distortion is limited to a certain desired level.

[0099] The present invention includes a preferred embodiment thatpermits a desired distortion level to be selected. This is achieved inpart by defining a window function w to limit a region where the uniqueand discrete mark may be introduced. This may be expressedmathematically by:

s=x+w(x,b)(ab−1 x)u,

[0100] where ${w\left( {x,b} \right)} = \left\{ \begin{matrix}0 & {{{if}\quad {bx}} > {a/l}} \\0 & {{{if}\quad {bx}} < {- K}} \\1 & {otherwise}\end{matrix} \right.$

[0101] The term K is known as a termination parameter because it definesa region outside of which the mark is not introduced and is the processis terminated. The first zero in the window function w corresponds to acase where the mark is correctly detected even without inserting anyadditional signal, implying that there is not need to increasedistortion. The second zero corresponds to a termination case.Specifically, if the original signal x is too strong and in the wrongdirection, the process is terminated and an error is allowed to occur.This allows this embodiment to guarantee a maximum distortion.

[0102] A new expected distortion may be computed as:E[D] = E[s − x] = E[w²(x, b)ab − 1x²s_(u)²] = s_(u)²∫_(−K)^(a)(a² + 1²x²)p(x)  x

[0103] The above equation illustrates that in order to have the samedistortion level D as existing spread spectrum techniques, the lastintegral should be equal to one. A simpler approach is to obtain anupper bound by extending the integrals to infinity. This makes thedistortion level D approximately the same as for existing spreadspectrum techniques, meaning that the distortion level D can beguaranteed (i.e., E[D]<s_(u) ²) by making:$a = {\sqrt{\frac{{Ns}_{u}^{2} - {1^{2}s_{x}^{2}}}{{Ns}_{u}^{2}}}.}$

[0104] In this case, an error probability p will be:

p=Pr{{circumflex over (b)}<0|b=1}=Pr{(x+m(x)(a−1x)+n<0)}≦Pr{x<−K}+Pr{−n>a+(1−1)x|x≦−K}Pr{x≦−K}

[0105] The second linear embedding parameter may be set equal to one(λ=1) in order to simplify analysis. In this situation the errorprobability becomes:

p≦Pr{x<−K}+Pr{n>a}Pr{x≧−K},

[0106] while for existing spread spectrum techniques the errorprobability is:

p≈Pr{x<−K}+Pr{n>1+x}Pr{x≧−K}

[0107] Therefore, the limited distortion embodiment of the presentinvention allows a distortion level to be limited while still providingimproved detection (i.e., lower error probability) over existing spreadspectrum techniques. This is accomplished by removing the influence ofthe original signal x from the detection. In addition, the limiteddistortion embodiment of the present invention allows a desireddistortion level to be selected by removing the influence of theoriginal signal x only over a pre-defined range.

[0108] Non-Linear Generic Embedding Function

[0109] In a preferred embodiment the present invention does not restrictthe generic embedding function μ(x,b) to a linear approximation. Thisoptimal case is more complex and more generic that the linearapproximation embodiment. Where the generic embedding function μ(x,b) isnot restricted to be linear, the marked signal s can be expressed as:

s=x+m(x,b)u.

[0110] As before, the goal is to find the optimum solution for thegeneric embedding function μ(x,b) that minimizes the error of thedetected encoding bit. One way to simplify the above equation is to notethat since the original signal x, the noise n, and the encoding bit bare independent, the generic embedding function μ(x,b) will be oddsymmetric. This means that μ(x,b)=−μ(−x,−b). Thus, for simplicity, theassumption may be made that the encoding bit b=1 such that the embeddingfunction is only a function of x. The generic embedding function may bewritten as μ(x) and the marked signal s may be expressed as:

s=x+m(x)u.

[0111] The distortion for a certain value of x is:

d(x)=(m(x))² s _(u) ².

[0112] And, as before, the sufficient statistic r (computed from y=s+n)may be represented as:

r(x)=x+m(x)+n.

[0113] The goal is to determine the generic embedding function μ(x) thatminimizes an expected detection error probability, p=E{pe(x)}, for agiven expected distortion D=E{d(x)}. The first step is to compute pe(x)as: $\begin{matrix}{{{pe}(x)} = {\Pr \left\{ {r < 0} \right\}}} \\{= {\Pr \left\{ {\left( {x + {m(x)} + n} \right) < 0} \right\}}} \\{= {\Pr \left\{ {n > {x + {m(x)}}} \right\}}} \\{= {\frac{1}{2}{{erfc}\left( \frac{x + {m(x)}}{S_{n}\sqrt{2}} \right)}}}\end{matrix}$

[0114] In order to be the optimum generic embedding function, μ(x) mustbe such that it satisfies:${\frac{\partial\quad}{\partial d}{{pe}(x)}} = K^{\prime}$

[0115] for some constant K′. Therefore an optimum solution μ(x) shouldsatisfy the equation: $\quad\left\{ \begin{matrix}{{{\frac{\partial\quad}{\partial m}{d(x)}} = 0},\quad {or}} \\{\frac{\frac{\partial\quad}{\partial m}{{pe}(x)}}{\frac{\partial\quad}{\partial m}{d(x)}} = K^{\prime}}\end{matrix} \right.$

[0116] Because d(x) is simply the (scaled) square of μ(x), the firstcondition is satisfied only for μ(x)=0. The second condition can berewritten as: $\begin{matrix}{\left. \Rightarrow\frac{\frac{\partial\quad}{\partial m}{{erfc}\left( \frac{x + {m(x)}}{s_{n}\sqrt{2}} \right)}}{2{m(x)}} \right. = \left. K^{\prime}\Rightarrow \right.} \\{{\left. \Rightarrow ^{- {(\frac{x + {m{(x)}}}{s_{n}\sqrt{2}})}^{2}} \right. = {{Km}(x)}},}\end{matrix}$

[0117] where K is a different constant. There is, unfortunately, noclosed form solution for μ(x) and the above equation must be solvednumerically.

[0118] A numerical solution for μ(x) can be found by first noting thatthe expected error probability depends on the variance of the noise, andon the constant K. Therefore, the constant K may be used as a parameterthat will determine a final balance between distortion and errorprobability. Depending on the values of K, s_(n), and x, the equationwill have one, two or three solutions, one of which is the optimum valueof μ (remember the equation is only a necessary condition). FIG. 7illustrates these three different cases. In particular, FIG. 7 shows aplot of the right side of the equation (a straight line) for a certain Kand the left side of the equation (a normal curve) for four differentvalues of x (namely, x=0, −3, −6, and −9). If positive values of x areused, the peak of curve will be offset to the left.

[0119] A solution (the optimal generic embedding function for the givenvalue of x) is one of the points where the normal curve intersects theline. For positive values of x the only intersection point must bechosen. However, as the value of x becomes more and more negative (i.e.,as the normal curve is offset more to the right) there will be two extraintersection points, both lying to the left of the peak. The middleintersection point may be discarded due to an increase in distortion andan increase in error probability that choice brings. In order to decidebetween a first and a third point, a ratio between the difference inerror probability and the difference in distortion at each point iscomputed.

[0120] Graphically, this can be interpreted as balancing the areasbetween the straight and the normal curves. In other words, the pointclosest to the origin is selected whenever the area between the curvesfrom this point to the second intersection point (i.e., the area inwhich the normal curve is below the straight line) is higher than thearea between the curves from the second to the third intersection points(i.e., the area in which the normal curve is above the straight line).Otherwise, the third intersection point is selected. In this way, anoptimal generic embedding function μ(x) is found numerically.

[0121] Redundant Bit Representation

[0122] In many situations the embedding system and method of the presentinvention may be used to embed the same mark in several differentoriginal signals. This may occur, for example, in the case where amanufacturer's mark is being embedded into several different songs. Oneproblem with this situation is that, if an attacker gains access toseveral of these marked signals, the marked signals may be averaged andthe mark may be detected through this averaging. Because the mark is thesame for all of the different original signals but the carrier signal isindependent, the mark will stand out and become easy to detect. All theattacker needs to have is enough signals having the same mark and thiscollusion attack can be used to detect the mark.

[0123] Several techniques exist for attenuating this collusion attackproblem. For example, one technique randomizes the starting point of themark insertion into the original signal. However, this requires adecoder to search for the starting point and therefore significantlyincreasing computational complexity. Other techniques currently used tomitigate the collusion attack problem also involve generally complexcomputational analysis for decoding.

[0124] The present invention addresses this problem by using a redundantbit representation. In particular, this redundant bit representation isimplemented so that a resulting average of marks tends to zero whenseveral original signals are averaged together. Many possibleimplementation of redundant bit representation may be used for thispurpose and will achieve similar results such that the averaging ofseveral original signals together will result in the average of markstending to zero.

[0125] A preferred embodiment of the present invention inserts an“invert” bit into the embedding process. This invert bit, which has 50%probability, indicates the need to invert any remaining bits. Forexample, if a original sequence of bits 0110101 needs to be inserted,then this original sequence is mapped into two bit sequences: 00110101and 11001010. Each of these two bit sequences is used in approximatelyhalf the original signals to be marked.

[0126] Because each one of these two sequences is the exact opposite ofthe other one, if an attacker average several marked signals together,the mark will not add constructively as before and will virtuallyeliminate this as a source of attack. More specifically, if N bits(b₁b₂b₃ . . . b_(N)) are to be transmitted, then the present inventiontransmits N+1 bits (a₀a₁a₂a₃ . . . a_(N)). In this embodiment, a₀ is arandom bit (with equal probability), and a_(i)=b_(i) XOR′a₀, for i=1, .. . N. It should be noted that several implementations of redundantrepresentation can be used to reduce collusion attacks and will achievesimilar results.

[0127] The foregoing description of the preferred embodiments of theinvention has been presented for the purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise form disclosed. Many modifications andvariations are possible in light of the above teaching. It is intendedthat the scope of the invention be limited not by this detaileddescription of the invention, but rather by the claims appended hereto.

1. A method for embedding information within a media, comprising:estimating interference of an original signal within the media with aninformation signal being embedded; modulating a strength of theinformation signal being embedded into the original signal to compensatefor the estimated interference of the original signal so as to minimizethe probability that the information signal cannot be detected;embedding the strength-modulated information signal into the originalsignal.
 2. The method of claim 1, wherein the information is a spreadspectrum sequence.
 3. The method of claim 2, wherein the spread spectrumsequence is pseudo random.
 4. (cancelled)
 5. The method of claim 1,wherein spread spectrum modulation is used to modulate the informationstrength.
 6. The method of claim 5, wherein the spread spectrummodulation uses an embedding function.
 7. (cancelled)
 8. The method ofclaim 6, wherein the embedding function is approximated by a linearfunction.
 9. The method of claim 6, wherein the embedding function is anonlinear function.
 10. The method of claim 6, further comprisingdetermining a optimal solution for the embedding function thatapproximately minimizes a probability of error in detection of anencoded bit.
 11. A method for a redundant representation of bits withina marked signals each containing an original signal and an embeddedinformation signal, comprising: embedding a non-inverted informationsignal into the original signal of approximately one-half of the markedsignals; and embedding an inverted information signal into the originalsignal of the remaining marked signals, thereby causing an average ofthe embedded information signals to tend toward zero when the markedsignals containing the embedded information signals are averagedtogether.
 12. (cancelled)
 13. A method for embedding information inanalog or digital media, comprising: receiving an original signal;applying a transformation to the received signal; estimating aninterference of the original signal within the media with an informationsignal being embedded therein; modulating a strength of the informationsignal being embedded into the original signal to compensate for theestimated interference of the original signal; embedding thestrength-modulated information signal into the original signal toproduce a marked signal; and applying the reverse of said transformationto the marked signal.
 14. The method of claim 13, wherein applying thetransformation includes converting the original signal to a domain moreappropriate to information embedding.
 15. The method of claim 13,wherein modulating the strength of the information signal includes usinga generic embedding function that approximately minimizes an error indetection of the embedded information signal in the original signal. 16.(cancelled)
 17. The method of claim 13, wherein the interference isestimated only over a pre-defined range.
 18. The method of claim 17,wherein a window function is established to define the pre-defined rangein which the embedded information may be embedded within the originalsignal.
 19. (cancelled)